Investigations of small world contact networks, defined as networks with a short characteristic path length and a substantial local clustering of contacts in the neighborhood of each node, have emphasized the process performance of such networks. The argument that large-scale, small world, contact networks are structures with startlingly efficient process performance is premised on the existence of shortcuts, without which the characteristic path lengths of the networks would be substantially larger. No doubt, given a high probability of transmission in each contact of a network, such shortcuts are a potential structural basis of reliable flows of information, influence, material and disease. However, interpersonal contacts are often markedly unreliable transmission conduits, and the average shortcut contact may be a more unreliable, episodic, transmission conduit than the average contact of cliques. With markedly unreliable contacts, fundamental helix substructures, that are parallel-transmission subsystems of the contact network, importantly enter into the analysis of network performance. These substructures of disjoint path redundancies are based on the local clustering of contacts in the neighborhoods of each node. Drawing on network reliability theory, this article presents an approach in which intersecting cliques of contact networks are a theoretically important construct in the specification of the transmission implications of observed contact networks. Clique intersections are a structural basis of path redundancies that enable reliable transmission among the nodes of contact networks consisting of contacts that may or may not be active conduits of transmissions during some period of time. The strong contacts that occur among clique members further enhance the contributions of these path redundancies.